arxiv: 2605.06513 · v1 · submitted 2026-05-07 · ❄️ cond-mat.soft

Recognition: unknown

Cooking crystalline candies and the ductile to brittle transition in concentrated suspensions

Andreia F. Silva , James A. Richards , Fiona Jeffrey , Rory E. O'Neill , Daniel J. M. Hodgson , Christopher Ness , Wilson C. K. Poon

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:24 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords crystalline candiesductile-brittle transitionconcentrated suspensionssolid volume fractionnon-Brownian particlesfrictional jammingrandom close packingboundary conditions

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The pith

Increasing the solid volume fraction of sugar crystals during cooking drives fudge from a ductile to a brittle solid, matching the same sequence in model calcite suspensions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that fudge prepared by boiling sugar, cream, and butter undergoes a clear mechanical progression as cooking time or temperature is increased: the mixture shifts from fluid-like behavior to a ductile solid that deforms without breaking, then to a brittle solid that fractures abruptly under compression. The authors propose that this sequence arises because the volume fraction of solid sugar crystals grows steadily during cooking. They reproduce the identical fluid-ductile-brittle progression in a laboratory suspension of non-Brownian calcite particles simply by raising the particle volume fraction from the frictional jamming point toward random close packing. Particle simulations further show that the details of the brittle response depend on the boundary conditions applied during mechanical testing.

Core claim

As cooking time or final cooking temperature increases, candies transition from a fluid to a ductile solid, then to a brittle solid that abruptly fractures in compression. This is proposed to be driven by rising solid sugar crystal volume fraction. The same sequence of behaviour is found in a suspension of non-Brownian calcite particles as the solid fraction moves from frictional jamming to random close packing. Particle-based simulations reveal the sensitivity of the observed phenomenon to boundary conditions.

What carries the argument

The solid volume fraction of crystals or particles, which governs the mechanical shift from frictional jamming to dense packing and the associated change from ductile to brittle response.

Load-bearing premise

That the mechanical transition in the candy is caused primarily by the increase in solid crystal volume fraction rather than by concurrent changes in the liquid matrix composition, protein denaturation, or other cooking-induced effects.

What would settle it

Preparing sugar-crystal suspensions at controlled solid fractions but with fixed liquid composition (no cooking) and checking whether the ductile-to-brittle transition occurs at the same volume-fraction values observed in the cooked fudge.

Figures

Figures reproduced from arXiv: 2605.06513 by Andreia F. Silva, Christopher Ness, Daniel J. M. Hodgson, Fiona Jeffrey, James A. Richards, Rory E. O'Neill, Wilson C. K. Poon.

**Figure 1.** Figure 1: FIG. 1. Cooking fudge. (a) Schematic thermal and compositional view at source ↗

**Figure 2.** Figure 2: FIG. 2. Compressional response of fudge cooked at increasing view at source ↗

**Figure 3.** Figure 3: FIG. 3. Shear rheology of fluid-solid transition. (a) Viscosity, view at source ↗

**Figure 5.** Figure 5: FIG. 5. Frictional particle simulations. (a) Strain dependence of devi view at source ↗

read the original abstract

The existence and origin of the ductile to brittle transition in non-Brownian suspensions and pastes is underexplored despite the ubiquity of such materials in practical applications. We demonstrate the phenomenon in candies of sugar crystals in a water-protein-fat matrix prepared by boiling a sugar-cream-butter mixture (known as 'fudge' in some countries). As cooking time or final cooking temperature increases, we observe a transition from a fluid to a ductile solid, then to a brittle solid that abruptly fractures in compression. We propose that this is driven by rising solid sugar crystal volume fraction, and indeed find the same sequence of behaviour in a suspension of non-Brownian calcite particles as the solid fraction moves from frictional jamming to random close packing. Particle-based simulations reveal the sensitivity of the observed phenomenon to boundary conditions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Fudge cooking gives an accessible demo of the ductile-brittle transition that lines up with calcite suspensions at increasing packing fraction, but the claim that crystal volume fraction is the main driver stays correlative without isolating matrix changes.

read the letter

The main point is that this paper turns ordinary fudge-making into a visible example of how concentrated suspensions shift from fluid to ductile to brittle as solid content rises, and they match the sequence in a controlled calcite system. That mapping, plus the simulation note on boundary conditions, is the fresh element here. It is not a big theoretical step but it gives a practical, low-tech way to see the transition that suspension researchers already know from other systems. Anyone can cook the candy at home and feel the change, which makes the physics more concrete than most lab pastes. The calcite runs are cleaner because the authors vary the solid fraction directly and recover the same progression from frictional jamming to random close packing. The simulations add that the observed fracture depends on how the material is confined, which is worth keeping in mind for real applications. The soft spot is the causal link in the candy itself. Longer cooking grows sugar crystals, but it also alters the liquid's viscosity, supersaturation, and interactions with the cream and butter proteins. The work does not report direct measurements of crystal volume fraction in the cooked samples or controls that hold the matrix fixed while changing only the solids. So the proposal that packing fraction drives the transition is plausible but not yet separated from other cooking effects. The calcite data stand on their own, yet the analogy back to fudge rests on that untested assumption. This is the kind of paper that could interest people working on non-Brownian suspensions or food processing who want a simple model system. It is not ready for citation in my own work, but the observations are solid enough and the system novel enough that it deserves peer review. Referees can ask for the missing fraction measurements and matrix controls, after which the central claim would be much stronger.

Referee Report

2 major / 2 minor

Summary. The manuscript reports qualitative observations of a fluid-to-ductile-to-brittle transition in fudge (a suspension of sugar crystals in a water-protein-fat matrix) as cooking time or final temperature is increased. The authors propose that the sequence is driven by rising solid sugar crystal volume fraction and reproduce the same progression in non-Brownian calcite suspensions as solid fraction increases from frictional jamming to random close packing. Particle-based simulations are presented to illustrate sensitivity to boundary conditions.

Significance. If the proposed mechanism holds, the work supplies an accessible experimental platform for investigating ductile-brittle transitions in concentrated suspensions, linking food processing to soft-matter mechanics. The reproduction of the sequence in a well-characterized model suspension together with the boundary-condition simulations constitutes a clear strength and provides a falsifiable route for further tests.

major comments (2)

[Abstract] Abstract: the central claim that the observed sequence 'is driven by rising solid sugar crystal volume fraction' rests on an untested causal attribution. No direct measurement of crystal volume fraction φ in the cooked fudge samples is reported, nor are control experiments described that hold matrix composition fixed while varying φ.
[Candy preparation and observation section] Candy preparation and observation section: concurrent changes in liquid supersaturation, viscosity, and protein/fat interactions occur with increased cooking time, yet these are not quantified or isolated from the proposed φ effect; this undermines the attribution of the transition solely to crystal fraction.

minor comments (2)

[Abstract] The abstract states that simulations 'reveal the sensitivity of the observed phenomenon to boundary conditions' but provides no further detail on simulation method, particle interactions, or specific boundary conditions tested.
[Figures and Methods] Figure captions and methods should explicitly state how crystal fraction was (or was not) estimated in the fudge and the precise solid fractions used in the calcite experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the work's significance and for the detailed, constructive comments. We respond to each major comment below, acknowledging where the manuscript can be improved.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the observed sequence 'is driven by rising solid sugar crystal volume fraction' rests on an untested causal attribution. No direct measurement of crystal volume fraction φ in the cooked fudge samples is reported, nor are control experiments described that hold matrix composition fixed while varying φ.

Authors: We agree that the manuscript does not report direct measurements of crystal volume fraction φ in the fudge, nor control experiments that isolate φ while holding other matrix properties fixed. The claim is presented as a proposal supported by the reproduction of the same sequence in the calcite model system, where φ is the controlled variable. We will revise the abstract, introduction, and discussion to state this limitation more explicitly, add references to literature on how cooking time affects crystallization in sugar mixtures, and emphasize that the model suspension provides the primary evidence for the role of φ. This is a partial revision, as new measurements on the original samples are not feasible. revision: partial
Referee: [Candy preparation and observation section] Candy preparation and observation section: concurrent changes in liquid supersaturation, viscosity, and protein/fat interactions occur with increased cooking time, yet these are not quantified or isolated from the proposed φ effect; this undermines the attribution of the transition solely to crystal fraction.

Authors: The referee is correct that cooking time alters multiple properties simultaneously. The fudge serves as a qualitative demonstration of the transition, while the controlled variation of solid fraction in the non-Brownian calcite suspension isolates the effect of φ. We will add a dedicated paragraph in the discussion section to acknowledge these concurrent changes in the candy system, explain why they are not isolated there, and clarify how the model experiments address the attribution. The text will be revised for greater precision on this point. revision: partial

Circularity Check

0 steps flagged

No circularity: independent experimental sequences and interpretive hypothesis

full rationale

The paper reports an observed fluid-ductile-brittle sequence in cooked fudge as a function of cooking time/temperature, proposes that rising crystal volume fraction φ is the driver, and tests the proposal by reproducing the same sequence in a separate, controlled calcite suspension system where φ is varied directly from frictional jamming to random close packing. This is an analogy between two distinct experimental systems rather than a derivation in which any prediction or result reduces by construction to its own inputs. No equations, fitted parameters renamed as predictions, self-definitional steps, or load-bearing self-citations appear in the abstract or described chain. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that solid volume fraction alone controls the observed mechanical sequence, with no explicit free parameters or new entities introduced in the abstract.

axioms (1)

domain assumption The ductile-to-brittle transition is driven by rising solid sugar crystal volume fraction
Proposed directly in the abstract as the explanation for the candy observations.

pith-pipeline@v0.9.0 · 5457 in / 1203 out tokens · 42179 ms · 2026-05-08T04:24:46.771992+00:00 · methodology

discussion (0)

Reference graph

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